Design of cumulative sum control schemes for truncated Poisson distribution

The cumulative sum (CUSUM) control chart procedures have proven to be more effective than the standard Shewhart control charts at detecting small shifts in mean under statistical control of any production processes. When one specific size of the mean shift is assumed, the CUSUM chart can be optimally designed in terms of average run length. In this paper, design and implementation procedures of CUSUM control schemes based on zero truncated Poisson distribution are given since zero truncated Poisson distribution has wide applications in industries. These truncated Poisson CUSUMs are easy to design and implement. The proposed design procedure can be used to detect both increasing and decreasing rate cases. The feature of fast initial response (FIR) of the truncated Poisson CUSUM is also discussed. Examples are also illustrated.